{"paper":{"title":"Invariant deformations of orbit closures in $\\mathfrak{sl}_n$","license":"","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Nicolas Ressayre (I3M), S\\'ebastien Jansou (I3M)","submitted_at":"2007-06-26T13:32:46Z","abstract_excerpt":"We study deformations of orbit closures for the action of a connected semisimple group $G$ on its Lie algebra $\\mathfrak{g}$, especially when $G$ is the special linear group. The tools we use are on the one hand the invariant Hilbert scheme and on the other hand the sheets of $\\mathfrak{g}$. We show that when $G$ is the special linear group, the connected components of the invariant Hilbert schemes we get are the geometric quotients of the sheets of $\\mathfrak{g}$. These quotients were constructed by Katsylo for a general semisimple Lie algebra $\\mathfrak{g}$; in our case, they happen to be af"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.3828","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}